How to stack multiple objects into a shape of another one?
Final result:



Overview:

You can use Particle System for such task. In my example you can see Suzanne and Cube filled with Spheres and Cube filled with Suzannes. 

Particle System setup:

First add Particle System to your object - the one that is volume/shape/emitter.

Setup it as in the picture below:




Start/End should be set to 0, so particles will be generated at one time,
Emit from Faces > Grid will assure that particles will be distributed evenly,
Resulotion - how many particles should be in the emitter,
Render > Object is an object you want to distribute,
Size is a size of this object.


Set this settings in Wireframe mode to see changes. After everything is as it should be, you can go to Modifiers tab and Convert Particle System to mesh. Then delete/hide your emitter object.



Edit:

Difference with high resolution between Emit from Faces and Volume:



Blend file: